It is important in both the medical fields, and in industry, to have the ability to non-invasively obtain images of interior portions of various objects, such as human organs, castings, and so forth. Particularly in the medical field, methods and apparatus for providing computer tomography (hereinafter CT) have evolved since about 1974, to relatively sophisticated two-dimensional (2-D) imaging systems. Such 2-D systems typically utilize a fan beam scanning mode for computer reconstruction of 2-D images. At present the most advanced CT devices, such as the Siemens SOMATOM, use a spiralling source--detector assembly and reconstruction is achieved from a series of 2-D slices. It is generally recognized that the next generation of CT devices will have to come from volume real time imaging for making examination possible, for example, of the palpitations of the heart. In order to achieve this, a speed up of both the data collection time and the reconstruction time are necessary. By using the full extent of an x-ray source producing a cone beam, and by using a surface detector such as an Image Intensifier in the Siemens MULTISKOP, data collection can indeed be speeded up significantly. However, a suitable high resolution fast 3-D reconstruction method with a large usable volume has yet to be devised. Although there are good iterative algebraic reconstruction methods which can be made very accurate, they usually take an inordinate amount of computer time to reach convergence.
Modern diagnostic radiology systems permit a radiologist to produce and interpret shadow images of internal organs of a human body, as indicated above. In such systems, x-radiation is used typically having an energy spectrum ranging from 50 to 200 keV, but in an industrial application significantly higher energy ranges may be used. Also in a typical diagnostic x-ray system a relatively broad beam of x-rays are utilized by passing them through an object, such as a section of a human body, whereby the rays exiting from the section of the body are impinged upon a detector. The detector typically may consist of photographic film or an x-ray detection tube. The x-rays are attenuated as they pass through a body, for example, according to the equation I=I.sub.0 e.sup.-.mu.x where I.sub.0 is the intensity of the x-ray beam, .mu. is an attenuation coefficient, and x is the thickness of the body. Since the attenuation coefficient .mu. is a function of the density of the material through the body and the atomic number thereof, various components of the body respectively attenuate the beam differently at different points as it passes through the body. These varying attenuation components of the x-ray beam exiting the body are detected as varying amounts of radiation. As a result, the detected beam provides a 2-D representation of the attenuation throughout the body.
A detector of photographic film provides a relatively high resolution permanent record or recorded image of the body. The resolution may approach 0.1 mm.
A disadvantage of such known systems is that only a 2-D representation is obtained of a 3-dimensional body.
Computerized tomography or tomographic systems have been developed for transmitting a relatively narrow x-ray beam through the body in a plane perpendicular to the axis of revolution. The detector is used to repetitively measure the total attenuation of the beam, typically thousands of times, with different rays being transmitted through the body in the same plane. Thousands of attenuation measurements are obtained across a narrow slice of a body in a plane perpendicular to the rotation axis. The sum of the attenuation through each of the segments along the beam path are representative of the attenuation of a narrow beam along the path. Accordingly, the total attenuation is equivalent to the sum of the attenuation of each segment.
In practice, for a given body slice being studied, the slices are divided into a plurality of pixels or surface elements. As a result, the attenuation measured at each of the pixels provides a measurement of the attenuation of the narrow beam through the body. Typical grid sizes or meshes of pixels are 512 by 512 matrices, requiring several hundred thousand measurements to be made to reproduce a given slice.
The data processing typically involves calculating the attenuation coefficient for each pixel element. The attenuation coefficients are typically normalized relative to a normalization of 1.0 for water, or some higher number for dense materials as found in bones, calcium for example. The normalization number for the water may be one thousand Hounsfield units, for example. The normalized coefficients are ranked in magnitude in accordance with a given scheme, whereafter a gray scale is assigned to the various computerized attenuation coefficients for displaying the slice on a view screen relative to a gray-scale ranking. As a result, a high resolution image showing small differences in tissue characteristics throughout the body are obtained. Similarly, for an industrial application of CT, other normalization criteria may apply.
In the most recent computerized tomographic systems three-dimensional (3-D) images are produced. Certain of these systems provide 3-D images from a plurality of 2-D slices taken in successive parallel planes. Other systems attempt to fill in gaps of data by using a plurality of 2-D slices obtained from a plurality of parallel planes taken along a first axis, and another plurality of slices of parallel planes taken along an axis perpendicular to the first axis. Regardless, such known systems still suffer from poor resolution as one moves away from a centralized focal point along an axis, due to gaps in the data obtained. Note that detectors other than photographic film are used in such modern systems. These detectors may include either ionization chambers filled with high-density gas, solid-state devices, or image intensifiers, for example.
Typically, in CT apparatus the x-ray source is conical, and a slit is generally put in front to make a fan beam source. For 3-D CT, the full extent of the x-ray source is used producing thus a cone beam. The beam pattern projected from the x-ray source is rotated about an object.
The present inventors recognized that in improving 3-D imaging, it is important to develop a truly 3-D reconstruction algorithm that provides both high resolution and fast reconstruction times. One known 3-D reconstruction algorithm has been developed by Feldkamp et al. (L. A. Feldkamp, L. C. Davis and J. W. Kress, "PRACTICAL CONE BEAM ALGORITHM", J. Opt. Soc. Am, 6 June 1984). The Feldkamp et al. algorithm, being basically an extension of the 2-D fan beam backprojection algorithm, is generally recognized by researchers as being very efficient. However, the present inventors discovered that because this algorithm only scans in the midplane, blurred images are produced at large vertical distances from the midplane, and that this deficiency is intrinsic to the scanning method.
Many attempts have been made in the prior art to provide 3-D tomography. For example, in Fencil et al. U.S. Pat. No. 4,875,165, a method for determination of 3-D structure in biplane angiography is described.
It was commonly thought that if one adds together scan data from two great circles that the "fuzziness" contributions of each would be additive, producing even greater fuzziness. The inventors disproved this by using the method of the present invention, whereby by adding together processed scan data from a plurality of great circle scans of an object, they discovered that fuzziness is actually reduced.